We received a number of solutions this month, many of which would get the right answer eventually, but only two which gave the "general equation". That is, one equation that works for any situation.

A lot of people managed to figure out the (5,3) solution as passing through seven squares, and then gave the equation as p + q - 1. That works, but fails to consider some "special cases" - like when the two numbers are the same, or when they have common factors (like (5,5) or (12,9)).

Most people dealt with these cases by writing new equations. Only two submissions presented an equation that would work for any situation, and those two are our winners for this month.

The first comes from the team TTN from the school V. Gimnazija, which is in Zagreb, Croatia. They decided to count the total intersections that the segment makes with the grid - the number of intersection minus one is the number of square that it goes through. A point was not considered an intersection, so they had to be subtracted as well. Their solution is very concise, and if you follow along with your own pencil and paper you'll see that they're right on. It's really very tidy. I would have liked to have heard more about how they figured it out, since that would help other students learn how to tackle a problem like this.

Our second winning entry comes from Tim Peterson, who goes to school at home in Rochester, New York. Tim started out by looking at some examples, including the "special cases", and worked from there. The method he used, of counting intersections, was a lot like the way that the other team used. He provides some good pictures and a pretty clear explanation. (He also uses a rather whimsical and timely background.)

Congratulations to both of our winners!

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